how to solve "Error using alpha. Too many output arguments."

I am getting "Error using alpha. Too many output arguments." after alpha3. Can someone help me resolve this?

%
clear all
close all
% Given
a=3;
b=13;
c=0;
rPA=b/2;
rPB=c/2;
theta2=100; % degrees
theta4=90; % degrees
omega2=2000*2*pi/60; % rpm
alpha2=10; % rad/s^2
w2=1; %lb
w3=2; %lb
w4=4; %lb
g=32.2;
m2=w2/g;
m3=w3/g;
m4=w4/g;
I2=0.02; %lb.ft.s^2
I3=0.08; %lb.ft.s^2
F=[-1000-500]; %lb
% Open Circuit
theta32=asind((-a*sind(theta2)+c)/b)+180;
d2=a*cosd(theta2)-b*cosd(theta32);
% Crossed Circuit
theta31=asind((a*sind(theta2)-c)/b);
d1=(a*cosd(theta2))-(b*cosd(theta31));
% Find torqe T12, pin force F12, pin force F32, pin force F43
theta3=asind((-a*sind(theta2)+c)/b)+180;
omega3=a*omega2*cosd(theta2)/(b*cosd(theta3));
ddot=-a*omega2*sind(theta2)+b*omega3*sind(theta3);
alpha3=(a*alpha*cosd(theta2)-a*omega2^2*sind(theta2)+b*omega3^2*sind(theta3))/(b*cosd(theta3));
Dddot=-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2)+b*alpha3*sind(theta3)+b*omega3^2*cosd(theta3);
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ab=[Dddot;0];
R2=a*[cosd(theta2);sind(theta2)];
R12=-R2/2;
R32=R2/2;
R3=b*[cosd(theta3);sind(theta3)];
R23=R3/2;
R43=-R3/2;
rG2=a/2;
rG3=b/2;
A2=[-rG2*alpha2*sind(theta2)-rG2*omega2^2*cosd(theta2); ...
 rG2*alpha2*cosd(theta2)-rG2*omega2^2*sind(theta2)];
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ag3a=[-rG3*alpha3*sind(theta3)-rG3*omega3^2*cosd(theta3);...
 rG3*alpha3*cosd(theta3)-rG3*omega3^2*sind(theta3)];
A3=Aa-Ag3a;
A4=[Dddot;0];
A=[1 0 1 0 0 0 0 0
 0 1 0 1 0 0 0 0
 -R12(2) R12(1) -R32(2) R32(1) 0 0 0 1
 0 0 -1 0 1 0 0 0
 0 0 0 -1 0 1 0 0
 0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0
 0 0 0 0 -1 0 mu 0
 0 0 0 0 0 -1 1 0];
B=[m2*A2(1)
 m2*A2(2)
 I2*alpha2
 m3*A3(1)
 m3*A3(2)
 I3*alpha3
 m4*A4(1)-F(1)
 -F(2)];
F=A\B

Answer 1

[KALYAN ACHARJYA]

#Done with some minor changed, also mu to m2 (There is no mu variable)

% Given
a=3;
b=13;
c=0;
rPA=b/2;
rPB=c/2;
theta2=100; % degrees
theta4=90; % degrees
omega2=2000*2*pi/60; % rpm
alpha2=10; % rad/s^2
w2=1; %lb
w3=2; %lb
w4=4; %lb
g=32.2;
m2=w2/g;
m3=w3/g;
m4=w4/g;
I2=0.02; %lb.ft.s^2
I3=0.08; %lb.ft.s^2
F=[-1000 -500]; %lb
% Open Circuit
theta32=asind((-a*sind(theta2)+c)/b)+180;
d2=a*cosd(theta2)-b*cosd(theta32);
% Crossed Circuit
theta31=asind((a*sind(theta2)-c)/b);
d1=(a*cosd(theta2))-(b*cosd(theta31));
% Find torqe T12, pin force F12, pin force F32, pin force F43
theta3=asind((-a*sind(theta2)+c)/b)+180;
omega3=a*omega2*cosd(theta2)/(b*cosd(theta3));
ddot=-a*omega2*sind(theta2)+b*omega3*sind(theta3);
alpha3=(a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)+b*omega3^2*sind(theta3))/(b*cosd(theta3));
Dddot=-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2)+b*alpha3*sind(theta3)+b*omega3^2*cosd(theta3);
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ab=[Dddot;0];
R2=a*[cosd(theta2);sind(theta2)];
R12=-R2/2;
R32=R2/2;
R3=b*[cosd(theta3);sind(theta3)];
R23=R3/2;
R43=-R3/2;
rG2=a/2;
rG3=b/2;
A2=[-rG2*alpha2*sind(theta2)-rG2*omega2^2*cosd(theta2); ...
 rG2*alpha2*cosd(theta2)-rG2*omega2^2*sind(theta2)];
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ag3a=[-rG3*alpha3*sind(theta3)-rG3*omega3^2*cosd(theta3);...
 rG3*alpha3*cosd(theta3)-rG3*omega3^2*sind(theta3)];
A3=Aa-Ag3a;
A4=[Dddot;0];
A=[1 0 1 0 0 0 0 0
   0 1 0 1 0 0 0 0
  -R12(2) R12(1) -R32(2) R32(1) 0 0 0 1
   0 0 -1 0 1 0 0 0
   0 0 0 -1 0 1 0 0
   0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0
   0 0 0 0 -1 0 m2 0
   0 0 0 0 0 -1 1 0];
B=[m2*A2(1)
   m2*A2(2)
   I2*alpha2
   m3*A3(1)
   m3*A3(2)
   I3*alpha3
   m4*A4(1)-F(1)
   -F(2)];
F=A\B

[Sencer Comert]

Thank you Kalyan very much for your help. I see what my simple mistake was! Now I get "index exceeds the number of arrays" error. It seems like you were able to solve for F.... here is the edited code:

%
clear all
close all
%Given
a=3;
b=13;
c=0;
theta2=100; % degrees
theta4=90; % degrees
omega2=2000*2*pi/60; % rpm
alpha2=10; % rad/s^2
w2=1; %lb
w3=2; %lb
w4=4; %lb
g=32.2;
m2=w2/g;
m3=w3/g;
m4=w4/g;
I2=0.02; %lb.ft.s^2
I3=0.08; %lb.ft.s^2
F=[-1000-500]; %lb
mu=0;
%Open Circuit
theta32=asind((-a*sind(theta2)+c)/b)+180;
d2=a*cosd(theta2)-b*cosd(theta32);
%Crossed Circuit
theta31=asind((a*sind(theta2)-c)/b);
d1=(a*cosd(theta2))-(b*cosd(theta31));
% Find torqe T12, pin force F12, pin force F32, pin force F43
theta3=asind((-a*sind(theta2)+c)/b)+180;
omega3=a*omega2*cosd(theta2)/(b*cosd(theta3));
ddot=-a*omega2*sind(theta2)+b*omega3*sind(theta3);
alpha3=(a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)+b*omega3^2*sind(theta3))/(b*cosd(theta3));
Dddot=-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2)+b*alpha3*sind(theta3)+b*omega3^2*cosd(theta3);
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ab=[Dddot;0];
R2=a*[cosd(theta2);sind(theta2)];
R12=-R2/2;
R32=R2/2;
R3=b*[cosd(theta3);sind(theta3)];
R23=R3/2;
R43=-R3/2;
rG2=a/2;
rG3=b/2;
A2=[-rG2*alpha2*sind(theta2)-rG2*omega2^2*cosd(theta2); ...
 rG2*alpha2*cosd(theta2)-rG2*omega2^2*sind(theta2)];
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ag3a=[-rG3*alpha3*sind(theta3)-rG3*omega3^2*cosd(theta3);...
 rG3*alpha3*cosd(theta3)-rG3*omega3^2*sind(theta3)];
A3=Aa-Ag3a;
A4=[Dddot;0];
A=[1 0 1 0 0 0 0 0
 0 1 0 1 0 0 0 0
 -R12(2) R12(1) -R32(2) R32(1) 0 0 0 1
 0 0 -1 0 1 0 0 0
 0 0 0 -1 0 1 0 0
 0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0
 0 0 0 0 -1 0 mu 0
 0 0 0 0 0 -1 1 0];
B=[m2*A2(1)
 m2*A2(2)
 I2*alpha2
 m3*A3(1)
 m3*A3(2)
 I3*alpha3
 m4*A4(1)-F(1)
 -F(2)];
F=A\B
% For 2 rev, plot torqe T12, pin force F12, pin force F32, pin force F43 on same graph as function of theta2
THETA2=0:1:360;
for i=1:1:length(THETA2)
 theta2=THETA2(i);
 theta3=asind((-a*sind(theta2)+c)/b)+180;
 omega3=a*omega2*cosd(theta2)/(b*cosd(theta3));
 alpha3=(a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)+b*omega3^2*sind(theta3))/(b*cosd(theta3));
 Dddot=-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2)+b*alpha3*sind(theta3)+b*omega3^2*cosd(theta3);
 Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
 Ab=[Dddot;0];
 g=32.2;
W2=1;
W3=2;
W4=4;
mu=0.4;
m2=W2/g;
m3=W3/g;
m4=W4/g;
I2=0.02;
I3=0.8;
F=[-1000;-500];
R2=a*[cosd(theta2);sind(theta2)];
R12=-R2/2;
R32=R2/2;
R3=b*[cosd(theta3);sind(theta3)];
R23=R3/2;
R43=-R3/2;
rG2=a/2;
rG3=b/2;
A2=[-rG2*alpha2*sind(theta2)-rG2*omega2^2*cosd(theta2); ...
 rG2*alpha2*cosd(theta2)-rG2*omega2^2*sind(theta2)];
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ag3a=[-rG3*alpha3*sind(theta3)-rG3*omega3^2*cosd(theta3);...
 rG3*alpha3*cosd(theta3)-rG3*omega3^2*sind(theta3)];
A3=Aa-Ag3a;
A4=[Dddot;0];
A=[1 0 1 0 0 0 0 0
 0 1 0 1 0 0 0 0
 -R12(2) R12(1) -R32(2) R32(1) 0 0 0 1
 0 0 -1 0 1 0 0 0
 0 0 0 -1 0 1 0 0
 0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0
 0 0 0 0 -1 0 mu 0
 0 0 0 0 0 -1 1 0];
B=[m2*A2(1)
 m2*A2(2)
 I2*alpha2
 m3*A3(1)
 m3*A3(2)
 I3*alpha3
 m4*A4(1)-F(1)
 -F(2)];
F=A\B;
T21(i)=-F(8);
f12(i)=norm([F(1);F(2)]);
f32(i)=norm([F(3);F(4)]);
f43(i)=norm([F(5);F(6)]);
end
plot(THETA2,T21,THETA2,f12,THETA2,f32,THETA2,f43)
grid minor
legend('T21','F12','F32','F43')
legend('Location','north')
set(gcf,'Visible','on')
grid minor

[KALYAN ACHARJYA]

%
a=3;
b=13;
c=0;
theta2=100; % degrees
theta4=90; % degrees
omega2=2000*2*pi/60; % rpm
alpha2=10; % rad/s^2
w2=1; %lb
w3=2; %lb
w4=4; %lb
g=32.2;
m2=w2/g;
m3=w3/g;
m4=w4/g;
I2=0.02; %lb.ft.s^2
I3=0.08; %lb.ft.s^2
F=[-1000 -500]; %lb
mu=0;
%Open Circuit
theta32=asind((-a*sind(theta2)+c)/b)+180;
d2=a*cosd(theta2)-b*cosd(theta32);
%Crossed Circuit
theta31=asind((a*sind(theta2)-c)/b);
d1=(a*cosd(theta2))-(b*cosd(theta31));
% Find torqe T12, pin force F12, pin force F32, pin force F43
theta3=asind((-a*sind(theta2)+c)/b)+180;
omega3=a*omega2*cosd(theta2)/(b*cosd(theta3));
ddot=-a*omega2*sind(theta2)+b*omega3*sind(theta3);
alpha3=(a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)+b*omega3^2*sind(theta3))/(b*cosd(theta3));
Dddot=-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2)+b*alpha3*sind(theta3)+b*omega3^2*cosd(theta3);
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ab=[Dddot;0];
R2=a*[cosd(theta2);sind(theta2)];
R12=-R2/2;
R32=R2/2;
R3=b*[cosd(theta3);sind(theta3)];
R23=R3/2;
R43=-R3/2;
rG2=a/2;
rG3=b/2;
A2=[-rG2*alpha2*sind(theta2)-rG2*omega2^2*cosd(theta2); ...
 rG2*alpha2*cosd(theta2)-rG2*omega2^2*sind(theta2)];
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ag3a=[-rG3*alpha3*sind(theta3)-rG3*omega3^2*cosd(theta3);...
 rG3*alpha3*cosd(theta3)-rG3*omega3^2*sind(theta3)];
A3=Aa-Ag3a;
A4=[Dddot;0];
A=[1 0 1 0 0 0 0 0
 0 1 0 1 0 0 0 0
 -R12(2) R12(1) -R32(2) R32(1) 0 0 0 1
 0 0 -1 0 1 0 0 0
 0 0 0 -1 0 1 0 0
 0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0
 0 0 0 0 -1 0 mu 0
 0 0 0 0 0 -1 1 0];
B=[m2*A2(1)
 m2*A2(2)
 I2*alpha2
 m3*A3(1)
 m3*A3(2)
 I3*alpha3
 m4*A4(1)-F(1)
 -F(2)];
F=A\B
% For 2 rev, plot torqe T12, pin force F12, pin force F32, pin force F43 on same graph as function of theta2
THETA2=0:1:360;
for i=1:1:length(THETA2)
 theta2=THETA2(i);
 theta3=asind((-a*sind(theta2)+c)/b)+180;
 omega3=a*omega2*cosd(theta2)/(b*cosd(theta3));
 alpha3=(a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)+b*omega3^2*sind(theta3))/(b*cosd(theta3));
 Dddot=-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2)+b*alpha3*sind(theta3)+b*omega3^2*cosd(theta3);
 Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
 Ab=[Dddot;0];
 g=32.2;
W2=1;
W3=2;
W4=4;
mu=0.4;
m2=W2/g;
m3=W3/g;
m4=W4/g;
I2=0.02;
I3=0.8;
F=[-1000;-500];
R2=a*[cosd(theta2);sind(theta2)];
R12=-R2/2;
R32=R2/2;
R3=b*[cosd(theta3);sind(theta3)];
R23=R3/2;
R43=-R3/2;
rG2=a/2;
rG3=b/2;
A2=[-rG2*alpha2*sind(theta2)-rG2*omega2^2*cosd(theta2); ...
 rG2*alpha2*cosd(theta2)-rG2*omega2^2*sind(theta2)];
Aa=[-a*alpha2*sind(theta2)-a*omega2^2*cosd(theta2); a*alpha2*cosd(theta2)-a*omega2^2*sind(theta2)];
Ag3a=[-rG3*alpha3*sind(theta3)-rG3*omega3^2*cosd(theta3);...
 rG3*alpha3*cosd(theta3)-rG3*omega3^2*sind(theta3)];
A3=Aa-Ag3a;
A4=[Dddot;0];
A=[1 0 1 0 0 0 0 0
 0 1 0 1 0 0 0 0
 -R12(2) R12(1) -R32(2) R32(1) 0 0 0 1
 0 0 -1 0 1 0 0 0
 0 0 0 -1 0 1 0 0
 0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0
 0 0 0 0 -1 0 mu 0
 0 0 0 0 0 -1 1 0];
B=[m2*A2(1)
 m2*A2(2)
 I2*alpha2
 m3*A3(1)
 m3*A3(2)
 I3*alpha3
 m4*A4(1)-F(1)
 -F(2)];
F=A\B;
T21(i)=-F(8);
f12(i)=norm([F(1);F(2)]);
f32(i)=norm([F(3);F(4)]);
f43(i)=norm([F(5);F(6)]);
end
plot(THETA2,T21,THETA2,f12,THETA2,f32,THETA2,f43)
grid minor
legend('T21','F12','F32','F43')
legend('Location','north')
set(gcf,'Visible','on')
grid minor

[Sencer Comert]

Thank you, Kalyan. I still get the "index exceeds the number of arrays" error. Is my matrix the problem?

A=[1 0 1 0 0 0 0 0

0 1 0 1 0 0 0 0

-R12(2) R12(1) -R32(2) R32(1) 0 0 0 1

0 0 -1 0 1 0 0 0

0 0 0 -1 0 1 0 0

0 0 R23(2) -R23(1) -R43(2) R43(1) 0 0

0 0 0 0 -1 0 mu 0

0 0 0 0 0 -1 1 0];

B=[m2*A2(1)

m2*A2(2)

I2*alpha2

m3*A3(1)

m3*A3(2)

I3*alpha3

m4*A4(1)-F(1)

-F(2)];

[KALYAN ACHARJYA]

Please copy my answer (code) and execute it

[Sencer Comert]

Thank you, Kalyan! :)